1. EE 3220: Digital Communication
Lec-3: Baseband transmission and Matched filter
Dr. Hassan Yousif Ahmed
Department of Electrical Engineering
College of Engineering at Wadi Aldwasser
Slman bin Abdulaziz University
Dr Hassan Yousif

2. Last time we talked about:
Transforming the information source to a form compatible with a digital system
Sampling
Aliasing
Quantization
Uniform and non-uniform
Baseband modulation
Binary pulse modulation
M-ary pulse modulation
M-PAM (M-ary Pulse amplitude modulation)‏
Dr Hassan Yousif

3. Formatting and transmission of baseband signal
Digital info.
Bit stream
(Data bits)‏
Pulse waveforms
(baseband signals)‏
Information (data) rate:
Symbol rate :
For real time transmission:
Textual
info.
Format
source
Pulse
modulate
Sample
Quantize
Encode
Analog
info.
Sampling at rate
(sampling time=Ts)‏
Encoding each q. value to
bits
(Data bit duration Tb=Ts/l)‏
Quantizing each sampled
value to one of the
L levels in quantizer.
Mapping every data bits to a
symbol out of M symbols and transmitting
a baseband waveform with duration T
Dr Hassan Yousif

4. Quantization example Quant. levels boundaries x(nTs): sampled values
amplitude
x(t)‏
x(nTs): sampled values
xq(nTs): quantized values
boundaries
Quant. levels
Ts: sampling time t
PCM
codeword
PCM sequence
Dr Hassan Yousif

5. Example of M-ary PAM
Assuming real time transmission and equal energy per transmission data bit for binary-PAM and 4-ary PAM:
4-ary: T=2Tb and Binary: T=Tb
Binary PAM
(rectangular pulse)‏
4-ary PAM
(rectangular pulse)‏ 3B A.
‘1’
‘11’ B T T
‘01’ T T
‘10’
‘00’ T T
‘0’ -B
-A.
-3B
Dr Hassan Yousif

6. Example of M-ary PAM … 2.2762 V 1.3657 V 1 1 0 1 0 1 Rb=1/Tb=3/Ts
Ts Ts
V V
0 Tb 2Tb 3Tb 4Tb 5Tb 6Tb
Rb=1/Tb=3/Ts
R=1/T=1/Tb=3/Ts
0 T T 3T 4T 5T 6T
Rb=1/Tb=3/Ts
R=1/T=1/2Tb=3/2Ts=1.5/Ts
T T T
Dr Hassan Yousif

7. Today we are going to talk about:
Receiver structure
Demodulation (and sampling)‏
Detection
First step for designing the receiver
Matched filter receiver
Correlator receiver
Dr Hassan Yousif

8. Demodulation and detection
Format
Pulse
modulate
Bandpass
modulate
M-ary modulation
channel
transmitted symbol
Major sources of errors:
Thermal noise (AWGN)‏
disturbs the signal in an additive fashion (Additive)
has flat spectral density for all frequencies of interest (White)‏
is modeled by Gaussian random process (Gaussian Noise)
Inter-Symbol Interference (ISI)‏
Due to the filtering effect of transmitter, channel and receiver, symbols are “smeared”.
estimated symbol
Format
Detect
Demod.
& sample
Dr Hassan Yousif

9. Example: Impact of the channel
Dr Hassan Yousif

10. Example: Channel impact …
Dr Hassan Yousif

11. Receiver tasks Demodulation and sampling: Detection:
Waveform recovery and preparing the received signal for detection:
Improving the signal power to the noise power (SNR) using matched filter
Reducing ISI using equalizer
Sampling the recovered waveform
Detection:
Estimate the transmitted symbol based on the received sample
Dr Hassan Yousif

12. Receiver structure Step 1 – waveform to sample transformation
Step 2 – decision making
Demodulate & Sample
Detect
Threshold
comparison
Frequency
down-conversion
Receiving
filter
Equalizing
filter
Compensation for channel induced ISI
For bandpass signals
Received waveform
Baseband pulse
(possibly distored)‏
Baseband pulse
Sample
(test statistic)‏
Dr Hassan Yousif

13. Baseband and bandpass
Bandpass model of detection process is equivalent to baseband model because:
The received bandpass waveform is first transformed to a baseband waveform.
Equivalence theorem:
Performing bandpass linear signal processing followed by heterodyning the signal to the baseband, yields the same results as heterodyning the bandpass signal to the baseband , followed by a baseband linear signal processing.
Dr Hassan Yousif

14. Steps in designing the receiver
Find optimum solution for receiver design with the following goals:
Maximize SNR
Minimize ISI
Steps in design:
Model the received signal
Find separate solutions for each of the goals.
First, we focus on designing a receiver which maximizes the SNR.
Dr Hassan Yousif

15. Design the receiver filter to maximize the SNR
Model the received signal
Simplify the model:
Received signal in AWGN
AWGN
Ideal channels
AWGN
Dr Hassan Yousif

16. Matched filter receiver
Problem:
Design the receiver filter such that the SNR is maximized at the sampling time when
is transmitted.
Solution:
The optimum filter, is the Matched filter, given by
which is the time-reversed and delayed version of the conjugate of the transmitted signal
Dr Hassan Yousif T t T t

17. Example of matched filterT 2T t
T/2 T t
T/2 T T t
T/2 T
3T/2 2T t
Dr Hassan Yousif

18. Properties of the matched filter
The Fourier transform of a matched filter output with the matched signal as input is, except for a time delay factor, proportional to the ESD of the input signal.
The output signal of a matched filter is proportional to a shifted version of the autocorrelation function of the input signal to which the filter is matched.
The output SNR of a matched filter depends only on the ratio of the signal energy to the PSD of the white noise at the filter input.
Two matching conditions in the matched-filtering operation:
spectral phase matching that gives the desired output peak at time T.
spectral amplitude matching that gives optimum SNR to the peak value.
Dr Hassan Yousif

19. Correlator receiver
The matched filter output at the sampling time, can be realized as the correlator output.
Dr Hassan Yousif

20. Implementation of matched filter receiver
Bank of M matched filters
Matched filter output:
Observation
vector
Dr Hassan Yousif

21. Implementation of correlator receiver
Bank of M correlators
Correlators output:
Observation
vector
Dr Hassan Yousif

22. Implementation example of matched filter receivers
Bank of 2 matched filters T t T T T t
Dr Hassan Yousif